Exploring the impact of thermal fluctuations on continuous models of adhesion

Adhesion and deadhesion processes at the interface between an object and a substrate are well-established phenomena in the realm of materials science and biophysics. These processes can be profoundly influenced by thermal fluctuations, a phenomenon empirically validated through numerous experimental observations. While discrete models have traditionally served as a foundation for understanding this intricate interplay, this paper seeks to bridge the gap between such discrete representations and the continuous models that more accurately reflect experimental scenarios. To achieve this objective, we initially adopt discrete models comprising n elements, selected such that their physical parameters converge towards the continuum limit as n approaches infinity. This thoughtful scaling ensures that the discrete system retains its relevance in the context of continuous media. Leveraging principles from Statistical Mechanics and Griffith-type total energy minimization approaches, we employ this scaled discrete model to investigate the impact of temperature in continuous adhesion phenomena. As a result, we obtain an analytical model to account for the decrease of the decohesion threshold depending on thermal (entropic) energy terms. Interestingly, our approach demonstrates that continuous adhesion models invariably exhibit phase transitions, whose critical temperatures can be derived through closed-form calculations. By elucidating these critical temperature values, this work enhances our understanding of adhesion processes within continuous media and opens new avenues for the exploration of adhesion-related phenomena in diverse scientific disciplines. Finally, the comparison with some experimental results is discussed